WHY-BRR

Why isn't brr mode automatically disabled when there are no
monitored runes? The reason is that the list of monitored runes is
kept in a wormhole state.

See wormhole for more information on wormholes in general. But
the fundamental property of the wormhole function is that it is a
logical no-op, a constant function that does not take state as an
argument. When entering a wormhole, arbitrary information can be
passed in (including the external state). That information is used
to construct a near copy of the external state and that ``wormhole
state'' is the one with respect to which interactions occur during
breaks. But no information is carried by ACL2 out of a wormhole --
if that were allowed wormholes would not be logical no-ops. The
only information carried out of a wormhole is in the user's head.

Break-rewrite interacts with the user in a wormhole state because
the signature of the ACL2 rewrite function does not permit it to
modify state. Hence, only wormhole interaction is possible. (This
has the additional desirable property that the correctness of the
rewriter does not depend on what the user does during interactive
breaks within it; indeed, it is logically impossible for the user to
affect the course of rewrite.)

Now consider the list of monitored runes. Is that kept in the
external state as a normal state global or is it kept in the
wormhole state? If it is in the external state then it can be
inspected within the wormhole but not changed. This is
unacceptable; it is common to change the monitored rules as the
proof attempt progresses, installing monitors when certain rules are
about to be used in certain contexts. Thus, the list of monitored
runes must be kept as a wormhole variable. Hence, its value cannot
be determined outside the wormhole, where the proof attempt is
ongoing.

This raises another question: If the list of monitored runes is
unknown to the rewriter operating on the external state, how does
the rewriter know when to break? The answer is simple: it breaks
every time, for every rune, if brr mode is enabled. The wormhole is
entered (silently), computations are done within the wormhole state
to determine if the user wants to see the break, and if so,
interactions begin. For unmonitored runes and runes with false
break conditions, the silent wormhole entry is followed by a silent
wormhole exit and the user perceives no break.

Thus, the penalty for running with brr mode enabled when there are
no monitored runes is high: a wormhole is entered on every
application of every rune and the user is simply unware of it. The
user who has finally unmonitored all runes is therefore strongly
advised to carry this information out of the wormhole and to do :brrnil in the external state when the next opportunity arises.